Publication

Impact from Black-Box Small-Signal State-Space Representation on Participation Factors Analysis

2025

Abstract

This paper investigates how black-box representation of sub-systems in a larger small-signal state-space model influences the results from participation factor analysis. The results show that the value of individual participation factors associated with the states of a black-box sub-system on diagonalized form can be misleading. To avoid this issue, participation factor analysis involving a black-boxed sub-system should be based on aggregation by the complex sum of participation factors associated with the subsystem. The reason is that individual participation factors of the diagonalized sub-system can assume high values that do not reflect a physical interaction with other sub-systems. However, the individual participation factors of any transparent part of the system model can still be studied according to established conventional methods. These findings are obtained from, and demonstrated by, analysis of the small-signal dynamics in an offshore islanded AC grid with two HVDC converter terminals applying grid forming control and two equivalent grid-following converters representing separate wind farm clusters.

Official source

https://infoscience.epfl.ch/entities/publication/ca16ebc0-c432-488e-ae5c-b797435a21df

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2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ca16ebc0-c432-488e-ae5c-b797435a21df

About this result

Related concepts (30)

Diagonalizable matrix

In linear algebra, a square matrix is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix and a diagonal matrix such that , or equivalently . (Such , are not unique.) For a finite-dimensional vector space , a linear map is called diagonalizable if there exists an ordered basis of consisting of eigenvectors of .

Diagonal matrix

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).

Jordan normal form

In linear algebra, a Jordan normal form, also known as a Jordan canonical form (JCF), is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to some basis. Such a matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal (on the superdiagonal), and with identical diagonal entries to the left and below them. Let V be a vector space over a field K.