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Experimental Investigation of the Hierarchical Control in DC Microgrids Using a Real-time Simulator
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Distributed Algorithm Design for Aggregative Games of Euler-Lagrange Systems and Its Application to Smart Grids.

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    This study introduces distributed algorithms for aggregative games with complex constraints, enabling autonomous decision-making in smart grid electricity markets to find equilibrium points.

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    Area of Science:

    • Control Theory
    • Game Theory
    • Distributed Systems

    Background:

    • Aggregative games feature coupled decision constraints.
    • Players in these games exhibit Euler-Lagrange (EL) dynamics.
    • Finding generalized Nash equilibrium (GNE) in such systems is challenging.

    Purpose of the Study:

    • To develop distributed algorithms for finding the variational generalized Nash equilibrium (GNE) in aggregative games.
    • To analyze the convergence properties of these algorithms.
    • To apply the developed methods to electricity market games in smart grids.

    Main Methods:

    • Utilized gradient descent, state feedback, and dynamic average consensus.
    • Employed singular perturbation analysis and variational analysis for convergence studies.
    • Developed two distinct distributed algorithms.

    Main Results:

    • The two algorithms achieve exponential and asymptotic convergence to the variational GNE, respectively.
    • Demonstrated autonomous GNE seeking for turbine-generator systems in smart grid electricity markets.
    • Simulation examples validated the effectiveness of the proposed methods.

    Conclusions:

    • The proposed distributed algorithms effectively solve variational GNE problems in aggregative games with EL dynamics.
    • The application to smart grids shows practical potential for autonomous market participation.
    • The convergence analysis provides theoretical guarantees for the algorithms' performance.