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.

翻译：本文研究了具有时变耦合不等式约束的电力系统分布式在线经济调度问题。该问题被建模为多智能体系统中的分布式在线优化问题。在每个时间步，每个智能体仅观测其自身的瞬时目标函数与局部不等式约束；智能体在线决策并协作，以在满足全局耦合约束的同时最小化时变目标函数之和。为解决该问题，我们提出一种基于原对偶方法并结合约束跟踪的算法。在目标函数与约束函数为凸函数、其梯度一致有界、且最优解序列的路径长度呈次线性增长等适当假设下，我们分析了所提算法的理论性质，证明了动态遗憾与约束违反量均相对于时间范围T呈次线性。最后，我们使用合成数据与澳大利亚能源市场数据，在电力系统时变经济调度问题上对所提算法进行了评估。结果表明，该算法在跟踪性能、约束满足度以及对时变扰动的适应性方面均表现有效，从而为实时分布式经济调度提供了一个实用且具有良好理论支撑的解决方案。