Oscillation characteristics and trajectory stability region analysis method of hierarchical control microgrids

Chen, Wei; Yang, Xusheng; Liao, Zhixian; Wu, Linlin; Qiu, Nan

doi:10.1016/j.egyr.2022.11.184

Cited by 3 publications

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The researchers, [52], discussed three possible scenarios, namely, stable, limit cycles and chaos arise naturally in the flow and thermal dynamics of the device. The authors, [53], formulated/initialized the cell model to the limit cycle, running one-dimensional (OD) simulations of 500 stimuli at a BCL of 300ms.In [54], the dynamic behaviour of the nonlinear system switches between a stable equilibrium point and a stable limit cycle has been discussed. In [55], the stable limit cycle has been observed in autocatalytic systems through the characteristics of the Hopf bifurcation.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Existence of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems

Patra

Patnaik

2023

International Journal of Applied Mathematics, Computational Science and Systems Engineering

View full text Add to dashboard Cite

The proposed work addresses the dynamics of a general system and explores the existence of limit cycles (LC) in multi-variable Non-linear systems with special attention to 3x3 nonlinear systems. It presents a simple, systematic analytical procedure as well as a graphical technique that uses geometric tools and computer graphics for the prediction of limit cycling oscillations in three-dimensional systems having both explicit and implicit nonlinear functions. The developed graphical method uses the harmonic balance/harmonic linearization for simplicity of discussion which provides a clear and lucid understanding of the problem and considers all constraints, especially the simultaneous intersection of two straight lines & one circle for determination of limit cycling conditions. The method of analysis is made simpler by assuming the whole system exhibits the limit cycling oscillations predominantly at a single frequency. The discussions made either analytically/graphically are substantiated by digital simulation by a developed program as well as by the use of the SIMULINK Toolbox of MATLAB Software.

show abstract

Section: Introductionmentioning

confidence: 99%

Investigation of the Existence of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems

Patra

Patnaik

2023

International Journal of Applied Mathematics, Computational Science and Systems Engineering

View full text Add to dashboard Cite

show abstract

Stability Analysis Method of a Hierarchical Control Structure Microgrid Based on a Small-Signal Model and Hopf Bifurcation Theory

Yang,

Chen,

et al. 2024

International Journal of Electrical Power & Energy Systems

View full text Add to dashboard Cite

Possibility of Quenching of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems

Patra,

Patnaik

2023

Wseas Transactions on Systems and Control

View full text Add to dashboard Cite

The present work proposes novel methods of Quenching self-sustained oscillations in the event of the existence of limit cycles (LC) in 3x3 non-linear systems. It explores the possibility of Stabilising/Quenching the LC by way of signal stabilization using high frequency dither signals both deterministic and random when 3X3 systems exhibit such self-sustained nonlinear oscillations under autonomous state. The present work also explores the suppression limit cycles of 3X3 systems using state feedback by either arbitrary pole placement or optimal selection of pole placement. The complexity involved, in implicit non-memory type nonlinearity for memory type nonlinearities, it is extremely difficult to formulate the problem. Under this circumstance, the harmonic linearization/harmonic balance reduces the complexity considerably. Furthermore, the method is made simpler assuming the whole 3X3 system exhibits the LC predominantly at a single frequency. It is equally a formidable task to make an attempt to suppress the limit cycles for 3X3 systems with memory type nonlinearity in particular. Backlash is one of the nonlinearities commonly occurring in physical systems that limit the performance of speed and position control in robotics, the automation industry, and other occasions of modern applications. The proposed methods are well illustrated through examples and substantiated by digital simulation (a program developed using MATLAB CODES) and the use of the SIMULINK Toolbox of MATLAB software.

show abstract

Oscillation characteristics and trajectory stability region analysis method of hierarchical control microgrids

Cited by 3 publications

References 17 publications

Investigation of the Existence of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems

Investigation of the Existence of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems

Stability Analysis Method of a Hierarchical Control Structure Microgrid Based on a Small-Signal Model and Hopf Bifurcation Theory

Possibility of Quenching of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems

Contact Info

Product

Resources

About