State Estimator Condition Number Analysis

A new algorithm for improving the numerical stability of power system state estimation

“…The decision of whether SE is well‐conditioned or ill‐conditioned is based on the value of a factor known as the condition number , which is a measure of the sensitivity of the gain/coefficient matrix and calculated as follows: where λ max and λ min are the maximum and minimum singular values, respectively, and are obtained from SVD. The condition number is close to unity for a well‐conditioned matrix, infinity for a singular matrix, and very high for an ill‐conditioned matrix .…”

Advancement of a long arithmetic technology in the construction of algorithms for studying linear systems

“…Up to now, quite a lot of precise and iterative methods for solving systems of linear algebraic equations have been developed. Specifically, some of them are listed in papers [3,4] and there exist many others. It may be stated that the problem of the development of a universal high-precision method for solving a wide class of linear problems has not been solved so far.…”

“…However, they do not solve the problem of the representation of numbers and implementation of operations for the numbers with more than 64 digits and it remains open. In this regard, for various kinds of ill-conditionality or the structure of the restriction matrix, there is a need to adapt the solution algorithm to ensure the computational quality [3][4][5].…”

“…takes large values that affect the errors of performing basic operations) [1][2][3][4][5]. It is possible to make sure that the information on the significance of the conditionality number (or its assessment) as a factor of control of calculation correctness currently remains in the scope of further research [3][4][5]. Specifically, the existence of the system conditionality control, accumulation of calculation errors when solving such inconvenient problems is a necessary and integral component of the computation process.…”

Influencia De La Topologia en El Condicionamiento De Matrices De Redes Eléctricas

“…En [5] se presenta un método algebraico que usa la factorización triangular de la matriz de ganancia simétrica para determinar las islas observables, a partir de un conjunto de mediciones para supervisión de un sistema de potencia. R. Ebrahimian y R. Baldick en [6] desarrollan fórmulas para el número de condición del problema de estimación de estado como una función con diferente tipo y número de medidas. En [7] se destaca la importancia del condicionamiento de matriz jacobiana en la validación de modelos de redes neuronales.…”