Distributed Extremum Seeking for Optimal Resource Allocation and Its Application to Economic Dispatch in Smart Grids

Area of Science:

• Optimization Algorithms
• Distributed Control Systems
• Resource Allocation
• Smart Grid Technology

Background:

• Decentralized resource allocation is crucial for efficient system operation.
• Existing methods often require detailed knowledge of cost functions and gradients.
• Need for robust algorithms that operate with limited local information.

Purpose of the Study:

• To develop a first-order extremum-seeking algorithm for resource allocation.
• To solve problems where local cost function forms and gradients are unknown.
• To ensure convergence to optimal solutions under resource constraints.

Main Methods:

• Utilizes measurements of local cost functions for optimization.
• Employs neighbor-to-neighbor communication under an undirected graph.
• Applies Lyapunov stability theory and average analysis for convergence proofs.

Main Results:

• The proposed first-order algorithm converges to the neighborhood of the optimal solution.
• The algorithm demonstrates semiglobally practically asymptotically stable behavior.
• A second-order extension with low-pass filters shows improved convergence performance.

Conclusions:

• The developed extremum-seeking algorithm effectively solves resource allocation problems without requiring explicit cost function information.
• The algorithm's stability and convergence are rigorously proven.
• Demonstrated practical applicability through numerical examples, including smart grid economic dispatch.