This paper is dedicated to solving the economic dispatch problem in smart grids, which aims at minimizing the total generation cost while satisfying the power supply-demand balance and generation capacity constraints. A distributed algorithm is proposed to solve the economic dispatch problem over directed communication topologies that are time-varying unbalanced. Its features are that the proposed algorithm is push-based, and the model of line losses is integrated into the problem of our interest to reduce the power losses. Resorting to geometric graph theory and convex analysis, it is proved that the incremental costs achieve consensus at a convergence rate $O({{1 / {\sqrt {t} }}})$ with $t$ being the number of iterations. Furthermore, robustness of the proposed algorithm is investigated solving the EDP when the communication information undergoes arbitrary large but bounded constant delays and the local gradients involve observation noises with zero-mean and bounded variance. Finally, three case studies implemented on an islanded microgrid, the IEEE 30-bus system and the IEEE 118-bus system are tested to demonstrate the effectiveness of the proposed algorithm.

中文翻译：

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基于时变不平衡有向图的智能电网中基于推送的分布式经济调度

本文致力于解决智能电网中的经济调度问题，其目标是在满足电力供需平衡和发电容量约束的同时，最小化总发电成本。提出了一种分布式算法来解决时变不平衡的有向通信拓扑结构上的经济调度问题。它的特点是所提出的算法是基于推送的，并且将线损模型集成到我们感兴趣的问题中以减少功率损耗。借助几何图论和凸分析，证明增量成本以收敛速度达成共识 $O({{1 / {\sqrt {t} }}})$ 和 $t$ 是迭代次数。此外，当通信信息经历任意大但有界的恒定延迟并且局部梯度涉及具有零均值和有界方差的观测噪声时，研究了所提出算法的稳健性来解决EDP。最后，对孤岛微电网、IEEE 30 总线系统和 IEEE 118 总线系统实施的三个案例研究进行了测试，以证明所提出算法的有效性。