Elimination of limit cycles in HVAC systems using the describing function method

2009 ◽  
Author(s):  
Jakob Rehrl ◽  
Martin Horn ◽  
Markus Reichhartinger
Keyword(s):  
Limit Cycles ◽  
Function Method ◽  
Hvac Systems ◽  
Describing Function ◽  
Describing Function Method

Application and Verification of Describing Function Method in Solving the Hunting Limit Cycles for Railway Vehicle

2011 ◽  
Vol 66-68 ◽  
pp. 1657-1662
Author(s):  
Chun Lei Hong ◽  
Yue Geng ◽  
Yong Sheng Hu
Keyword(s):  
Limit Cycles ◽  
Function Method ◽  
Degrees Of Freedom ◽  
Engineering Application ◽  
Railway Vehicle ◽  
Describing Function ◽  
Vehicle Model ◽  
Strongly Nonlinear ◽  
Practical Engineering ◽  
Describing Function Method

It is presented to solve the hunting limit cycles of railway system with multiple degrees of freedom and strongly nonlinear factors by describing function method(DFM). A nonlinear railway vehicle model with several dry friction factors is developed, and the 16 nonlinear transcendental equations of it are deduced using DFM. The modal characteristics of the hunting limit cycle for the vehicle model are obtained by the software programmed to solve complicated equation set. To verify the accuracy of describing function method, the hunting limit cycles of the model are simulated in time domain, and the results from these two methods have good consistence. This shows that the limit cycles of nonlinear rail vehicle systems with strongly nonlinear factors can be solved with high accuracy and efficiency by DFM, which of value in practical engineering application.

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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