Augmented Matrix

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Joerg Schaaf - One of the best experts on this subject based on the ideXlab platform.

  • Maxwell–Stefan model of multicomponent ion transport inside a monolayer Nafion membrane for intensified chlor-alkali electrolysis
    2019
    Co-Authors: R. R. Sijabat, S Moshtarikhah, M T De Groot, Joerg Schaaf
    Abstract:

    Abstract: A mathematical model based on a generalized Maxwell–Stefan equation has been developed to describe multicomponent ion and water transport inside a cation-exchange membrane. This model has been validated using experimental data and has been used to predict concentration profiles, membrane potential drop, and transport numbers of ions and water for the chlor-alkali process at increased current densities. Several improvements have been made to previously developed Maxwell–Stefan models. In our model, the generalized Maxwell–Stefan equation is written in terms of concentration instead of mole fraction and the fixed group (membrane) concentration is assumed to be constant. We have adapted the Augmented Matrix method using the built-in partial differential equation parabolic elliptic (pdepe) solver in Matlab®, and both the concentration and the electrical potential gradients have been solved simultaneously. The boundary conditions are determined with the Donnan equilibrium at the membrane–solution interface. We have also employed semi-empirical correlations to define the Maxwell–Stefan diffusivities inside the membrane. For the bulk diffusivities, we applied the correlations for the concentrated solution instead of the values at infinite dilution. With the diffusivities presented in this work, the model shows a better fit to the experimental data than with previously reported fitted diffusivities. Prediction of the sodium transport number and water transport number is generally good, whereas the deviations with regard to membrane potential might also be related to issues with the experimental data. The model predicts an increase in both sodium and water transport numbers at increased current density operation of chlor-alkali production. Graphical abstract: [Figure not available: see fulltext.].

Kwang Y Lee - One of the best experts on this subject based on the ideXlab platform.

  • a new eigen sensitivity theory of Augmented Matrix and its applications to power system stability analysis
    2000
    Co-Authors: Haekon Nam, Yongku Kim, Kwanshik Shim, Kwang Y Lee
    Abstract:

    In this paper, a new second-order eigen-sensitivity and perturbation theory of the Augmented Matrix is developed using of only dominant eigenvalues and their left and right-eigenvectors. Eigen-sensitivities on various system and control parameters are computed for the analysis of small signal and voltage stability of the New England power system. It is also shown that the sensitivity analysis may be used as an invaluable tool for analysis, planning, and operation of power systems: identification of the cause of the stability problems and weak lines; optimal tuning of control parameters; determining locations of compensating devices for stability enhancement such as capacitor compensation and FACTS devices.

Robert Caiming Qiu - One of the best experts on this subject based on the ideXlab platform.

  • A Correlation Analysis Method for Power Systems Based on Random Matrix Theory
    2017
    Co-Authors: Xinyi Xu, Xing He, Qian Ai, Robert Caiming Qiu
    Abstract:

    The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems. In this situation, the model-based methods need to be revisited. A data-driven method, as the novel alternative on the other hand, is proposed in this paper. It reveals the correlations between the factors and the system status through statistical properties of data. An Augmented Matrix as the data source is the key trick for this method and is formulated by two parts: (1) status data as the basic part; and (2) factor data as the Augmented part. The random Matrix theory is applied as the mathematical framework. The linear eigenvalue statistics, such as the mean spectral radius, are defined to study data correlations through large random matrices. Compared with model-based methods, the proposed method is inspired by a pure statistical approach without a prior knowledge of operation and interaction mechanism models for power systems and factors. In general, this method is direct in analysis, robust against bad data, universal to various factors, and applicable for real-time analysis. A case study based on the standard IEEE 118-bus system validates the proposed method.

  • a correlation analysis method for power systems based on random Matrix theory
    2015
    Co-Authors: Robert Caiming Qiu
    Abstract:

    The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems; in this situation, the modelbased methods need be revisited. A data-driven method, as the novel alternative, on the other hand, is proposed in this paper: it reveals the correlations between the factors and the system status through statistical properties of data. An Augmented Matrix, as the data source, is the key trick for this method; it is formulated by two parts: 1) status data as the basic part, and 2) factor data as the Augmented part. The random Matrix theory (RMT) is applied as the mathematical framework. The linear eigenvalue statistics (LESs), such as the mean spectral radius (MSR), are defined to study data correlations through large random matrices. Compared with model-based methods, the proposed method is inspired by a pure statistical approach, without a prior knowledge of operation and interaction mechanism models for power systems and factors. In general, this method is direct in analysis, robust against bad data, universal to various factors, and applicable for real-time analysis. A case study, based on the standard IEEE 118-bus system, validates the proposed method.

R. R. Sijabat - One of the best experts on this subject based on the ideXlab platform.

  • Maxwell–Stefan model of multicomponent ion transport inside a monolayer Nafion membrane for intensified chlor-alkali electrolysis
    2019
    Co-Authors: R. R. Sijabat, S Moshtarikhah, M T De Groot, Joerg Schaaf
    Abstract:

    Abstract: A mathematical model based on a generalized Maxwell–Stefan equation has been developed to describe multicomponent ion and water transport inside a cation-exchange membrane. This model has been validated using experimental data and has been used to predict concentration profiles, membrane potential drop, and transport numbers of ions and water for the chlor-alkali process at increased current densities. Several improvements have been made to previously developed Maxwell–Stefan models. In our model, the generalized Maxwell–Stefan equation is written in terms of concentration instead of mole fraction and the fixed group (membrane) concentration is assumed to be constant. We have adapted the Augmented Matrix method using the built-in partial differential equation parabolic elliptic (pdepe) solver in Matlab®, and both the concentration and the electrical potential gradients have been solved simultaneously. The boundary conditions are determined with the Donnan equilibrium at the membrane–solution interface. We have also employed semi-empirical correlations to define the Maxwell–Stefan diffusivities inside the membrane. For the bulk diffusivities, we applied the correlations for the concentrated solution instead of the values at infinite dilution. With the diffusivities presented in this work, the model shows a better fit to the experimental data than with previously reported fitted diffusivities. Prediction of the sodium transport number and water transport number is generally good, whereas the deviations with regard to membrane potential might also be related to issues with the experimental data. The model predicts an increase in both sodium and water transport numbers at increased current density operation of chlor-alkali production. Graphical abstract: [Figure not available: see fulltext.].

  • Maxwell–Stefan model of multicomponent ion transport inside a monolayer Nafion membrane for intensified chlor-alkali electrolysis
    2019
    Co-Authors: R. R. Sijabat, M T De Groot, Moshtari Khah S Shohreh, Schaaf, John J Van Der
    Abstract:

    \u3cp\u3eAbstract: A mathematical model based on a generalized Maxwell–Stefan equation has been developed to describe multicomponent ion and water transport inside a cation-exchange membrane. This model has been validated using experimental data and has been used to predict concentration profiles, membrane potential drop, and transport numbers of ions and water for the chlor-alkali process at increased current densities. Several improvements have been made to previously developed Maxwell–Stefan models. In our model, the generalized Maxwell–Stefan equation is written in terms of concentration instead of mole fraction and the fixed group (membrane) concentration is assumed to be constant. We have adapted the Augmented Matrix method using the built-in partial differential equation parabolic elliptic (pdepe) solver in Matlab®, and both the concentration and the electrical potential gradients have been solved simultaneously. The boundary conditions are determined with the Donnan equilibrium at the membrane–solution interface. We have also employed semi-empirical correlations to define the Maxwell–Stefan diffusivities inside the membrane. For the bulk diffusivities, we applied the correlations for the concentrated solution instead of the values at infinite dilution. With the diffusivities presented in this work, the model shows a better fit to the experimental data than with previously reported fitted diffusivities. Prediction of the sodium transport number and water transport number is generally good, whereas the deviations with regard to membrane potential might also be related to issues with the experimental data. The model predicts an increase in both sodium and water transport numbers at increased current density operation of chlor-alkali production. Graphical abstract: [Figure not available: see fulltext.].\u3c/p\u3

M T De Groot - One of the best experts on this subject based on the ideXlab platform.

  • Maxwell–Stefan model of multicomponent ion transport inside a monolayer Nafion membrane for intensified chlor-alkali electrolysis
    2019
    Co-Authors: R. R. Sijabat, S Moshtarikhah, M T De Groot, Joerg Schaaf
    Abstract:

    Abstract: A mathematical model based on a generalized Maxwell–Stefan equation has been developed to describe multicomponent ion and water transport inside a cation-exchange membrane. This model has been validated using experimental data and has been used to predict concentration profiles, membrane potential drop, and transport numbers of ions and water for the chlor-alkali process at increased current densities. Several improvements have been made to previously developed Maxwell–Stefan models. In our model, the generalized Maxwell–Stefan equation is written in terms of concentration instead of mole fraction and the fixed group (membrane) concentration is assumed to be constant. We have adapted the Augmented Matrix method using the built-in partial differential equation parabolic elliptic (pdepe) solver in Matlab®, and both the concentration and the electrical potential gradients have been solved simultaneously. The boundary conditions are determined with the Donnan equilibrium at the membrane–solution interface. We have also employed semi-empirical correlations to define the Maxwell–Stefan diffusivities inside the membrane. For the bulk diffusivities, we applied the correlations for the concentrated solution instead of the values at infinite dilution. With the diffusivities presented in this work, the model shows a better fit to the experimental data than with previously reported fitted diffusivities. Prediction of the sodium transport number and water transport number is generally good, whereas the deviations with regard to membrane potential might also be related to issues with the experimental data. The model predicts an increase in both sodium and water transport numbers at increased current density operation of chlor-alkali production. Graphical abstract: [Figure not available: see fulltext.].

  • Maxwell–Stefan model of multicomponent ion transport inside a monolayer Nafion membrane for intensified chlor-alkali electrolysis
    2019
    Co-Authors: R. R. Sijabat, M T De Groot, Moshtari Khah S Shohreh, Schaaf, John J Van Der
    Abstract:

    \u3cp\u3eAbstract: A mathematical model based on a generalized Maxwell–Stefan equation has been developed to describe multicomponent ion and water transport inside a cation-exchange membrane. This model has been validated using experimental data and has been used to predict concentration profiles, membrane potential drop, and transport numbers of ions and water for the chlor-alkali process at increased current densities. Several improvements have been made to previously developed Maxwell–Stefan models. In our model, the generalized Maxwell–Stefan equation is written in terms of concentration instead of mole fraction and the fixed group (membrane) concentration is assumed to be constant. We have adapted the Augmented Matrix method using the built-in partial differential equation parabolic elliptic (pdepe) solver in Matlab®, and both the concentration and the electrical potential gradients have been solved simultaneously. The boundary conditions are determined with the Donnan equilibrium at the membrane–solution interface. We have also employed semi-empirical correlations to define the Maxwell–Stefan diffusivities inside the membrane. For the bulk diffusivities, we applied the correlations for the concentrated solution instead of the values at infinite dilution. With the diffusivities presented in this work, the model shows a better fit to the experimental data than with previously reported fitted diffusivities. Prediction of the sodium transport number and water transport number is generally good, whereas the deviations with regard to membrane potential might also be related to issues with the experimental data. The model predicts an increase in both sodium and water transport numbers at increased current density operation of chlor-alkali production. Graphical abstract: [Figure not available: see fulltext.].\u3c/p\u3