scholarly journals Chaotic Synchronization in a Small Network of a Class of Power Systems via Contraction Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
G. Solís-Perales ◽  
E. Ruiz-Velázquez ◽  
J. A. García-Rodríguez
Keyword(s):  
Nonlinear Systems ◽  
Power Systems ◽  
State Space ◽  
Stability Theory ◽  
Chaotic Synchronization ◽  
The State ◽  
Auxiliary System ◽  
Analysis Method ◽  
Virtual System ◽  
Contraction Theory

This paper presents a synchronization analysis of networks of a class of power systems using the contraction theory for nonlinear systems. This analysis is characterized by not being based on Lyapunov's stability theory, that is, it is not required to determine a Lyapunov candidate function. Moreover, from the contraction conditions, robustness of the synchronization can be obtained, in this sense, the analysis method is robust. The analysis consists in identifying or proposing a virtual or auxiliary system which is contracting in a region of the state space. It is intended that in this region the trajectories of the systems on the network converge to those of the virtual system and then obtain the synchronization of the systems in the network. The contribution consists in applying this nontraditional analysis to the problem of chaotic synchronization of a network of a class of power systems.

scholarly journals Modeling interconnected ICT and power systems for resilience analysis

2020 ◽  
Vol 3 (S1) ◽  
Author(s):  
Amit Dilip Patil ◽  
Jonas Haack ◽  
Martin Braun ◽  
Hermann de Meer
Keyword(s):  
Power Systems ◽  
State Space ◽  
System Performance ◽  
Hierarchical Modeling ◽  
Energy System ◽  
The State ◽  
Essential Property ◽  
Modeling Approach ◽  
Physical Energy ◽  
The Impact

Abstract Increasing interdependencies between power and ICT systems amplify the possibility of cascading failures. Resilience against such failures is an essential property of modern and sustainable power systems and networks. To assess the resilience and predict the behaviour of a system consisting of interdependent subsystems, the interconnection requires adequate modeling. This work presents an approach to model and determine the state of these so-called interconnectors in future cyber-physical energy systems with strongly coupled ICT and power systems for a resilience analysis. The approach can be used to capture the impact of various parameters on system performance upon suitable modification. An hierarchical modeling approach is developed with atomic models that demonstrate the interdependencies between a power and ICT system. The modeling approach using stochastic activity nets is applied to an exemplary redispatch process in a cyber-physical energy system. The performance of an interconnector when facing limited performance from the ICT subsystem and its subsequent impact on the power system is analysed using the models. The state of the interconnector, as well as the service level are mapped to a resilience state-space diagram. The representation of system state on the resilience state-space diagram allows interpretation of system performance and quantification of resilience metrics.

A Direct Approach to Order Reduction of Nonlinear Systems Subjected to External Periodic Excitations

2008 ◽  
Vol 3 (3) ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
State Space ◽  
Invariant Manifold ◽  
Large Scale ◽  
Reduction Process ◽  
Order Reduction ◽  
The State ◽  
Reduced Order Models ◽  
External Excitation ◽  
Reduced Order

In this work, the basic problem of order reduction of nonlinear systems subjected to an external periodic excitation is considered. This problem deserves special attention because modes that interact (linearly or nonlinearly) with external excitation dominate the response. These dominant modes are identified and chosen as the “master” modes to be retained in the reduction process. The simplest idea could be to use a linear approach such as the Guyan reduction and choose those modes whose natural frequencies are close to that of external excitation as the master modes. However, this technique does not guarantee accurate results when nonlinear interactions are strong and a nonlinear approach must be adopted. Recently, the invariant manifold technique has been extended to forced problems by “augmenting” the state space, i.e., forcing is treated as an additional state and an invariant manifold is constructed. However, this process does not provide a clear picture of possible resonances and conditions under which an order reduction is possible. In a direct innovative approach suggested here, a nonlinear time-dependent relationship between the dominant and nondominant states is assumed and the dimension of the state space remains the same. This methodology not only yields accurate reduced order models but also explains the consequences of various primary and secondary resonances present in the system. One obtains various reducibility conditions in a closed form, which show interactions among eigenvalues, nonlinearities and the external excitation. One can also recover all “resonance conditions” obtained via perturbation or averaging techniques. The “linear” as well as the “extended invariant manifold” techniques are applied to some typical problems and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control of large-scale externally excited nonlinear systems.

Measuring the Direction and the Strength of Coupling in Nonlinear Systems—A Modeling Approach in the State Space

2004 ◽  
Vol 11 (7) ◽  
pp. 617-620 ◽  
Author(s):  
B. Veeramani ◽  
K. Narayanan ◽  
A. Prasad ◽  
L.D. Iasemidis ◽  
A.S. Spanias ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
State Space ◽  
The State ◽  
Modeling Approach

Computational Issues In a Nonlinear Observer for Systems With Quantized Outputs

1997 ◽  
Vol 119 (3) ◽  
pp. 528-535
Author(s):  
D. Shevitz ◽  
B. Paden
Keyword(s):  
Kalman Filter ◽  
Computational Complexity ◽  
Nonlinear Systems ◽  
State Space ◽  
Data Structures ◽  
Nonlinear Filtering ◽  
Recursive Algorithm ◽  
The State ◽  
Nonlinear Observer ◽  
Numerical Implementation

In this paper we develop an observer for nonlinear systems with quantized outputs. The observer is a recursive algorithm based on the intersection of sets: each measurement defines a set in state space which, by recursive intersection, is used to refine knowledge of the state. We develop the necessary data structures and procedures to implement the algorithm numerically. Comparisons are drawn between the proposed observer, the Kalman filter, and the equations of nonlinear filtering. Estimates are given for the error due to the triangulation of the set of consistent states and the computational complexity of the numerical implementation of our observer. Finally, the algorithm is applied to two example systems.

An Algebraically Derived Nonlinear Control Theory

1983 ◽  
Vol 105 (2) ◽  
pp. 83-91 ◽  
Author(s):  
A. J. Fish ◽  
D. Jordan
Keyword(s):  
Nonlinear Systems ◽  
Control Theory ◽  
Nonlinear Control ◽  
State Space ◽  
Large Class ◽  
Hybrid Systems ◽  
The State ◽  
System Model ◽  
Nonlinear Control Theory ◽  
New System

This paper presents a control theory, for a large class of nonlinear systems, including analog, digital, and hybrid systems. The control theory is developed from a new system model that can be used to model nonlinear systems that cannot be modeled with the state space equations.

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