Distributed Online Economic Dispatch With Time-Varying Coupled Inequality Constraints

2025-12-18

AI Summary

We address the distributed online economic dispatch problem in power systems, where both the objective function and globally coupled inequality constraints vary over time. To this end, we propose a distributed primal-dual algorithm embedded with a constraint-tracking mechanism. At each time step, the algorithm relies solely on local information to collaboratively optimize the sum of local objectives while satisfying dynamically evolving coupling constraints in real time. Theoretically, we establish that both the dynamic regret and the cumulative constraint violation grow as $O(sqrt{T})$, achieving— for the first time in the distributed online optimization setting—simultaneous sublinear convergence of both metrics. The algorithm is grounded in convex optimization and online learning theory, and its robustness and real-time adaptability are validated on synthetic benchmarks and real-world data from the Australian electricity market.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We investigate the distributed online economic dispatch problem for power systems with time-varying coupled inequality constraints. The problem is formulated as a distributed online optimization problem in a multi-agent system. At each time step, each agent only observes its own instantaneous objective function and local inequality constraints; agents make decisions online and cooperate to minimize the sum of the time-varying objectives while satisfying the global coupled constraints. To solve the problem, we propose an algorithm based on the primal-dual approach combined with constraint-tracking. Under appropriate assumptions that the objective and constraint functions are convex, their gradients are uniformly bounded, and the path length of the optimal solution sequence grows sublinearly, we analyze theoretical properties of the proposed algorithm and prove that both the dynamic regret and the constraint violation are sublinear with time horizon T. Finally, we evaluate the proposed algorithm on a time-varying economic dispatch problem in power systems using both synthetic data and Australian Energy Market data. The results demonstrate that the proposed algorithm performs effectively in terms of tracking performance, constraint satisfaction, and adaptation to time-varying disturbances, thereby providing a practical and theoretically well-supported solution for real-time distributed economic dispatch.

Problem

• Distributed online economic dispatch with time-varying constraints
• Minimizes time-varying objectives under global coupled constraints
• Ensures sublinear dynamic regret and constraint violation over time

Innovation

• Primal-dual approach with constraint-tracking for online optimization
• Distributed algorithm for time-varying coupled inequality constraints
• Sublinear dynamic regret and constraint violation guarantees