scholarly journals Newton-Raphson State Estimation Solution Employing Systematically Constructed Jacobian Matrix

10.5772/8200 ◽  
2009 ◽  
Author(s):  
Nursyarizal Mohd ◽  
Ramiah Jegatheesan ◽  
Ir. Perumal
Keyword(s):  
State Estimation ◽  
Jacobian Matrix ◽  
Newton Raphson

Mixed Measurement State Estimation of the Equivalent Current Transformation Based on Generalized Tellegen's Theorem

2013 ◽  
Vol 373-375 ◽  
pp. 970-975
Author(s):  
Gui Hua Lin ◽  
Tao Wang ◽  
Yu Ying Wang ◽  
Li Guo Zheng
Keyword(s):  
State Estimation ◽  
Numerical Stability ◽  
Stability Problem ◽  
Jacobian Matrix ◽  
Estimation Method ◽  
Constant Matrix ◽  
Equivalent Current ◽  
Scada System ◽  
Current State ◽  
Secondary Factor

One of the most important ways to enhance the speed of state estimation is to establish the constant matrix Jacobian. This essay puts forward the state estimation method of the equivalent current transformation based on the Generalized Tellegens Theorem. This estimation method establishes the constant Jacobian matrix without neglecting the secondary factor making use of the Generalized Tellegens Theorem, solves the numerical stability problem caused by the establishment of the constant Jacobian matrix in the current state estimation, and has the advantages of a relatively rapid computing rate, making advantage of measuremnt of WAMS and SCADA system, and an unparalleled astringency. The method put forward in this essay has been verified through IEEE-30 Node System, and the efficiency of it has been fully proved by the example results.

scholarly journals Toeplitz Jacobian Method for Nonlinear Double-Periodic Excitations

1997 ◽  
Vol 4 (5-6) ◽  
pp. 351-359
Author(s):  
T. Ge ◽  
A.Y.T. Leung
Keyword(s):  
Jacobian Matrix ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Response Characteristics ◽  
Excited System ◽  
Newton Raphson ◽  
Complete Frequency ◽  
Steady State Solutions ◽  
Raphson Iteration ◽  
Continuation Technique

The Toeplitz Jacobian matrix method is an efficient algorithm for computing the steady state solutions of nonlinear periodic vibration. In this paper, the method is generalized by using multiple time scales to double-periodic solutions in a multi-frequency excited system. The method is combined with a standard multi-dimensional FFT algorithm to accurately simulate the nonlinear oscillators with widely separated frequencies. The continuation technique can also be incorporated with the Newton–Raphson iteration to further increase its efficiency, and to achieve the complete frequency response characteristics.

Application of the Newton-Raphson Method in a Voice Localization System

2014 ◽  
Vol 513-517 ◽  
pp. 4435-4438
Author(s):  
Ming Yu Tong ◽  
Di Jian Xu ◽  
Jin Liang Shi ◽  
Yan Shi
Keyword(s):  
Nonlinear Equations ◽  
Jacobian Matrix ◽  
Initial Solution ◽  
Test Results ◽  
Localization System ◽  
Voice Source ◽  
Solution Of Equations ◽  
Newton Raphson ◽  
The Voice ◽  
Raphson Method

In a voice localization system, the nonlinear equation of voice sources coordinates were established according the accepted information, so the algorithm for solving nonlinear equations is the key problem to the voice source localization syetem. In this paper, the Newton - Raphson method (N-R) is applied to solve the nonlinear equations, by setting the initial solution of equations,then calculating the unbalance vector and Jacobian matrix (J) so as to attain corrected vetor, after modification and iteration the initial solution,until meet the precision numerical solution. Test results show that, application of N-R method in voice localization system have advantange of less number of iterations, saving chip resources and high precision, can meet the precision requirements of voice localization system.

State Estimation of Equivalent Current Measurement Transformation Based on Generalized Tellegen's Theorem

2013 ◽  
Vol 732-733 ◽  
pp. 941-947 ◽  
Author(s):  
Gui Hua Lin ◽  
Yan Jun Zhang ◽  
Tao Wang ◽  
Yu Ying Wang
Keyword(s):  
State Estimation ◽  
Numerical Stability ◽  
Stability Problem ◽  
Jacobian Matrix ◽  
Estimation Method ◽  
Constant Matrix ◽  
Equivalent Current ◽  
Current State ◽  
Secondary Factor ◽  
Measurement Transformation

One of the most important ways to enhance the speed of state estimation is to establish the constant matrix Jacobian. This essay puts forward the state estimation method of the equivalent current transformation based on the Generalized Tellegen’s Theorem. This estimation method establishes the constant Jacobian matrix without neglecting the secondary factor making use of the Generalized Tellegen’s Theorem, solves the numerical stability problem caused by the establishment of the constant Jacobian matrix in the current state estimation, and has the advantages of a relatively rapid computing rate and an unparalleled astringency. The method put forward in this essay has been verified through IEEE-30 Node System, and the efficiency of it has been fully proved by the example results.

State Estimation Observability Based on the Null Space of the Measurement Jacobian Matrix

2005 ◽  
Vol 20 (3) ◽  
pp. 1656-1658 ◽  
Author(s):  
E. Castillo ◽  
A.J. Conejo ◽  
R.E. Pruneda ◽  
C. Solares
Keyword(s):  
State Estimation ◽  
Jacobian Matrix ◽  
Null Space
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