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Control of coupled oscillator networks with application to microgrid technologies
Per Sebastian Skardal1, Alex Arenas2
1Department of Mathematics, Trinity College, Hartford, CT 06106, USA. ; Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain.
Science Advances
|November 25, 2015
Summary
Researchers developed a control method for complex systems, specifically networks of coupled phase oscillators, to achieve stable synchronization. The number of oscillators needed for control depends on coupling strength and network dynamics, not structure.
Area of Science:
- Mathematics and Physics
- Engineering and Applied Sciences
Background:
- Complex systems and network-coupled dynamical systems are crucial in mathematics and physics.
- Smart grid technologies motivate research into controlling synchronization in these systems.
- Networks of coupled phase oscillators with nonlinear interactions are a key model for self-organization.
Purpose of the Study:
- To develop a method for controlling synchronization in networks of coupled phase oscillators.
- To identify and stabilize problematic oscillators to achieve a stable synchronized state.
Main Methods:
- Developing a control strategy focused on identifying and stabilizing specific oscillators within the network.
- Analyzing the resulting spectrum of eigenvalues to ensure linear stability of the synchronized state.
Main Results:
- A method was developed to achieve a linearly stable synchronized state in networks of coupled phase oscillators.
- The required amount of control is primarily determined by coupling strength, dynamical heterogeneity, and mean network degree.
- Network structural heterogeneity has minimal impact on the control effort needed.
Conclusions:
- The proposed control method effectively stabilizes synchronization in complex oscillator networks.
- Understanding the interplay between network properties and control is vital for applications like smart grids.
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