Inverse matrix modification lemma and Thévenin theorem for compensated network solutions

1999 ◽  
Vol 146 (5) ◽  
pp. 496 ◽  
Author(s):  
G.L. Pasini ◽  
M. Montagna ◽  
G.P. Granelli
Keyword(s):  
Inverse Matrix ◽  
Matrix Modification

scholarly journals Fault Current Constraint Transmission Expansion Planning Based on the Inverse Matrix Modification Lemma and a Valid Inequality

Energies ◽  
2019 ◽  
Vol 12 (24) ◽  
pp. 4769
Author(s):  
Sungwoo Lee ◽  
Hyoungtae Kim ◽  
Tae Hyun Kim ◽  
Hansol Shin ◽  
Wook Kim
Keyword(s):  
Current Level ◽  
Inverse Matrix ◽  
Valid Inequality ◽  
Fault Current ◽  
Impedance Matrix ◽  
Expansion Planning ◽  
Transmission Expansion Planning ◽  
Fault Currents ◽  
Transmission Expansion ◽  
Matrix Modification

In the transmission expansion planning (TEP) problem, it is challenging to consider a fault current level constraint due to the time-consuming update process of the bus impedance matrix, which is required to calculate the fault currents during the search for the optimal solution. In the existing studies, either a nonlinear update equation or its linearized version is used to calculate the updated bus impedance matrix. In the former case, there is a problem in that the mathematical formulation is derived in the form of mixed-integer nonlinear programming. In the latter case, there is a problem in that an error due to the linearization may exist and the change of fault currents in other buses that are not connected to the new transmission lines cannot be detected. In this paper, we use a method to obtain the exact updated bus impedance matrix directly from the inversion of the bus admittance matrix. We propose a novel method based on the inverse matrix modification lemma (IMML) and a valid inequality is proposed to find a better solution to the TEP problem with fault current level constraint. The proposed method is applied to the IEEE two-area reliability test system with 96 buses to verify the performance and effectiveness of the proposed method and we compare the results with the existing methods. Simulation results show that the existing TEP method based on impedance matrix modification method violates the fault current level constraint in some buses, while the proposed method satisfies the constraint in all buses in a reasonable computation time.

scholarly journals The Drazin inverse matrix modification formulae with Peirce corners

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2605-2616
Author(s):  
Daochang Zhang ◽  
Dijana Mosic ◽  
Jianping Hu
Keyword(s):  
Inverse Matrix ◽  
Drazin Inverse ◽  
Special Cases ◽  
Matrix Modification ◽  
Additive Perturbation ◽  
Special Matrix

Our motivation is to derive the Drazin inverse matrix modification formulae utilizing the Drazin inverses of adequate Peirce corners under some special cases, and the Drazin inverse of a special matrix with an additive perturbation. As applications, several new results for the expressions of the Drazin inverses of modified matrices A ?? CB and A ?? CDdB are obtained, and some well known results in the literature, as the Sherman-Morrison-Woodbury formula and Jacobson?s Lemma, are generalized.

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

scholarly journals Progresses in Food Packaging, Food Quality, and Safety—Controlled-Release Antioxidant and/or Antimicrobial Packaging

Molecules ◽  
2021 ◽  
Vol 26 (5) ◽  
pp. 1263
Author(s):  
Cornelia Vasile ◽  
Mihaela Baican
Keyword(s):  
Food Quality ◽  
Food Packaging ◽  
Life Extension ◽  
Quality And Safety ◽  
Testing Methods ◽  
Food Handling ◽  
Active Food Packaging ◽  
Matrix Modification ◽  
Radiofrequency Identification ◽  
Food Quality And Safety

Food packaging is designed to protect foods, to provide required information about the food, and to make food handling convenient for distribution to consumers. Packaging has a crucial role in the process of food quality, safety, and shelf-life extension. Possible interactions between food and packaging are important in what is concerning food quality and safety. This review tries to offer a picture of the most important types of active packaging emphasizing the controlled/target release antimicrobial and/or antioxidant packaging including system design, different methods of polymer matrix modification, and processing. The testing methods for the appreciation of the performance of active food packaging, as well as mechanisms and kinetics implied in active compounds release, are summarized. During the last years, many fast advancements in packaging technology appeared, including intelligent or smart packaging (IOSP), (i.e., time–temperature indicators (TTIs), gas indicators, radiofrequency identification (RFID), and others). Legislation is also discussed.

Inverse Matrix Autosearch Technique for the RTS MIMO OTA Test

2020 ◽  
pp. 1-8
Author(s):  
Penghui Shen ◽  
Yihong Qi ◽  
Wei Yu ◽  
Fuhai Li
Keyword(s):  
Inverse Matrix
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