[Paper Review] Sparsity-Constrained Games and Distributed Optimization with Applications to Wide-Area Control of Power Systems.

Feier Lian, Alexandra Duel‐Hallen+1 more|arXiv (Cornell University)|May 2, 2016

Distributed Control Multi-Agent Systems27 references3 citations

TL;DR

This paper proposes a sparsity-constrained differential game framework for distributed wide-area control in power systems, using GraSP and gradient descent to compute Nash equilibria under limited communication. It enables cost-effective, sparse sensor-controller networks in multi-area power systems while ensuring distributed optimization and fair cost allocation.

ABSTRACT

Multi-agent networked dynamic systems attracted attention of researchers due to their ability to model spatially separated or self-motivated agents. In particular, differential games are often employed to accommodate different optimization objectives of the agents, but their optimal solutions require dense feedback structures, which result in high costs of the underlying communication network. In this work, social linear-quadratic-regulator (LQR) optimization and differential games are developed under a constraint on the number of feedback links among the system nodes. First, a centralized optimization method that employs the Gradient Support Pursuit (GraSP) algorithm and a restricted Newton step was designed. Next, these methods are combined with an iterative gradient descent approach to determine a Nash Equilibrium (NE) of a linear-quadratic game where each player optimizes its own LQR objective under a shared global sparsity constraint. The proposed noncooperative game is solved in a distributed fashion with limited information exchange. Finally, a distributed social optimization method is developed. The proposed algorithms are used to design a sparse wide-area control (WAC) network among the sensors and controllers of a multi-area power system and to allocate the costs of this network among the power companies. The proposed algorithms are analyzed for the Australian 50-bus 4-area power system example.

Motivation & Objective

• To address the high communication cost of dense feedback in multi-agent dynamic systems by enforcing sparsity in feedback links.
• To develop a distributed algorithm that computes Nash equilibria under a global sparsity constraint for linear-quadratic games.
• To enable fair cost allocation among power companies for the deployment of a sparse wide-area control network.
• To apply the framework to real-world power system examples, specifically the Australian 50-bus 4-area system.
• To combine centralized optimization with distributed iterative methods for scalable and practical implementation.

Proposed method

• A centralized optimization method is designed using the Gradient Support Pursuit (GraSP) algorithm to identify the sparsest feedback structure satisfying the sparsity constraint.
• A restricted Newton step is employed to refine the solution and improve convergence in the centralized phase.
• The method integrates iterative gradient descent to compute a Nash equilibrium in a noncooperative linear-quadratic game with shared sparsity constraints.
• The algorithm is adapted for distributed implementation, where each agent only exchanges limited information with neighbors to compute its optimal control strategy.
• A distributed social optimization method is developed to allocate the total network cost among power companies based on their contributions to the sparse control network.
• The framework is applied to the Australian 50-bus 4-area power system to validate performance and scalability.

Experimental results

Research questions

• RQ1 How can a distributed Nash equilibrium be computed in a linear-quadratic differential game when the number of feedback links is constrained?
• RQ2 What is the trade-off between control performance and communication cost in wide-area power system control under sparsity constraints?
• RQ3 Can a distributed algorithm achieve near-optimal performance while maintaining low communication overhead in multi-area power systems?
• RQ4 How can the cost of deploying a sparse wide-area control network be fairly allocated among multiple power companies?
• RQ5 What is the impact of sparsity constraints on the stability and convergence of distributed control algorithms in power systems?

Key findings

• The proposed algorithm successfully computes a Nash equilibrium under a global sparsity constraint using a combination of GraSP and iterative gradient descent.
• The distributed implementation achieves convergence with limited information exchange, making it scalable for large power systems.
• The sparse wide-area control network design reduces communication costs significantly compared to dense feedback structures.
• The cost allocation mechanism fairly distributes network deployment costs among power companies based on their participation in the control network.
• The method was validated on the Australian 50-bus 4-area power system, demonstrating practical feasibility and performance under real-world constraints.
• The restricted Newton step improves convergence speed and solution quality in the centralized phase of the algorithm.