With recent advancements in network technologies like 5G and Internet of Things (IoT), the size and complexity of networked interconnected agents have increased rapidly. Although centralized schemes have simpler algorithm design, in practicality, it creates high computational complexity and requires high bandwidth for centralized data pooling. In this dissertation, for distributed optimization of networked multi-agent architecture, the Alternating Direction Method of Multipliers (ADMM) is investigated. In particular, a new adaptive-gain ADMM algorithm is derived in closed form and under the standard convex property to greatly speed up the convergence of ADMM-based distributed optimization. Using the Lyapunov direct approach, the proposed solution embeds control gains into a weighted network matrix among the agents uses and those weights as adaptive penalty gains in the augmented Lagrangian. For applications in a smart grid where system parameters are greatly affected by intermittent distributed energy resources like Electric Vehicles (EV) and Photo-voltaic (PV) panels, it is necessary to implement the algorithm in real-time since the accuracy of the optimal solution heavily relies on sampling time of the discrete-time iterative methods. Thus, the algorithm is further extended to the continuous domain for real-time applications and the convergence is proved also through Lyapunov direct approach. The algorithm is implemented on a distribution grid with high EV penetration where each agent exchanges relevant information among the neighboring nodes through the communication network, optimizes a combined convex objective of EV welfare and voltage regulation with power equations as constraints. The algorithm falls short when the dynamic equations like EVs state of charge are taken into account. Thus, the algorithm is further developed to incorporate dynamic constraints and the convergence along with control law is developed using Lyapunov direct approach. An alternative approach for convergence using passivity-short properties is also shown. Simulation results are included to demonstrate the effectiveness of proposed schemes.
Doctor of Philosophy (Ph.D.)
College of Engineering and Computer Science
Electrical and Computer Engineering
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Rahman, Towfiq, "Distributed Multi-agent Optimization and Control with Applications in Smart Grid" (2020). Electronic Theses and Dissertations, 2020-. 400.