In this paper, the economic dispatch problem (EDP) in smart grids is investigated over a directed network, which concentrates on allocating the generation power among the generators to satisfy the load demands with minimal total generation cost while complying with all constraints of local generation capacity. Each generator possesses its own local generation cost, and the total generation cost is the sum of all local generation costs. To deal with EDP, most of the existing methods, such as strategy based on push-sum, surmount the unbalancedness induced by the directed network via employing column-stochastic weights, which might be infeasible in distributed implementation. In contrast, in order to be suitable for the directed network with row-stochastic weights, we develop a novel directed distributed Lagrangian momentum algorithm, named as D-DLM, which integrates distributed gradient tracking method with two types of momentum terms and utilizes non-uniform step-sizes with respect to the updates of Lagrangian multipliers. If the largest step-size and the maximum momentum coefficient are positive and sufficiently small, D-DLM can linearly allocate the optimal dispatch on condition that the generation costs are smooth and strongly convex. Finally, a variety of studies on EDP in smart grids are simulated.

中文翻译：

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在有向网络上实现智能电网分布式经济调度的加速

在本文中，智能电网中的经济调度问题 (EDP) 在有向网络上进行了研究，该网络集中于在发电机之间分配发电功率以满足负载需求，同时满足本地发电容量的所有约束，同时总发电成本最小. 每个发电机都有自己的本地发电成本，总发电成本是所有本地发电成本的总和。为了处理EDP，现有的大多数方法，例如基于推和的策略，通过使用列随机权重来克服有向网络引起的不平衡，这在分布式实现中可能是不可行的。相比之下，为了适用于具有行随机权重的有向网络，我们开发了一种新颖的有向分布式拉格朗日动量算法，命名为 D-DLM，它将分布式梯度跟踪方法与两种动量项相结合，并利用非均匀步长来更新拉格朗日乘子。如果最大步长和最大动量系数为正且足够小，则 D-DLM 可以在生成成本平滑且强凸的条件下线性分配最优调度。最后，对智能电网中 EDP 的各种研究进行了模拟。