FIRST HARMONIC ANALYSIS OF PLANAR LINEAR SYSTEMS WITH SINGLE SATURATED FEEDBACK

1996 ◽  
Vol 06 (12b) ◽  
pp. 2605-2610 ◽  
Author(s):  
RODOLFO SUÁREZ ◽  
JOSÉ ALVAREZ-RAMIREZ ◽  
BALTAZAR AGUIRRE
Keyword(s):  
Linear Systems ◽  
Periodic Orbits ◽  
Function Method ◽  
Open Loop ◽  
Control Parameters ◽  
Describing Function ◽  
Open Loop System ◽  
Unstable Eigenvalue ◽  
Unstable Equilibrium Point ◽  
Describing Function Method

A first harmonic approach (describing function method) is used here to analyze the dependence of periodic orbits on the control parameters of planar linear systems with single saturated feedback. It is shown that, if the open-loop system has at least one unstable eigenvalue, periodic orbits converge monotonically to an unstable equilibrium point as the control gains go to infinity.

Harmonic Loss Calculation of Three-Phase Transformer Based on J-A Model

2013 ◽  
Vol 325-326 ◽  
pp. 519-524
Author(s):  
Lian Liu ◽  
Qiong Lin Li ◽  
Hui Jin Liu ◽  
Xue Cui ◽  
Lei Zou
Keyword(s):  
Maxwell Equations ◽  
Function Method ◽  
Domain Model ◽  
Iron Core ◽  
Describing Function ◽  
Good Convergence ◽  
Proposed Model ◽  
Three Phase ◽  
Describing Function Method ◽  
Transformer Model

Beginning with characterizing the nonlinearities of transformer, this paper uses the J-A model to represent the hysteresis of iron core, and fits the model in calculating exciting current. Compared with the other methods, such as polynomial and describing function method, J-A model is more capable in representing nonlinearity, so the calculated current would be more accurate. Then, after analyzing Maxwell equations that meet certain boundary conditions, the paper considers comprehensively the effects of skin and proximity, and then obtains the computing way of ac resistance under harmonics. At last, based on the mentioned results, paper proposes a set of three-phase transformer model which could calculate harmonic losses. The proposed model is a kind of combined time-and frequency-domain model that possesses good convergence. The introduced example has verified the correctness and effectiveness of the model which absolutely suits the engineering applications.

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