Abstract We consider the problem of distributed secondary frequency regulation in power networks such that stability and an optimal power allocation are guaranteed. This is a problem that has been widely studied in the literature, where two main control schemes have been proposed, usually referred to as ’Primal-Dual’ and ’distributed averaging proportional–integral (DAPI)’ respectively. However, each has its limitations, with the former incorporating additional information flow requirements which may limit its applicability, and with the existing literature on the latter relying on static models for generation and demand, which is restrictive. We propose a novel control scheme that aims to overcome these issues by making use of generation measurements in the control policy. In particular, our controller relies on practical measurements and allows distributed stability and optimality guarantees to be deduced for a broad range of linear generation dynamics, that can be of higher order. We show how the controller parameters can be selected in a computationally efficient way by solving appropriate linear matrix inequalities (LMIs). Furthermore, we demonstrate how the proposed analysis applies to various examples of turbine governor dynamics by using realistic numerical data. The practicality of our analysis is demonstrated with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system that verify that our proposed controller achieves convergence to the nominal frequency, an economically optimal power allocation, and improved performance compared to existing schemes used in the literature.

中文翻译：

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具有稳定性保证和最优功率分配的二次频率控制分布式方案

摘要 我们考虑了电网中分布式二次调频问题，以保证稳定性和最佳功率分配。这是一个在文献中被广泛研究的问题，其中提出了两种主要的控制方案，通常分别称为“原始对偶”和“分布式平均比例积分（DAPI）”。然而，每个都有其局限性，前者包含可能限制其适用性的额外信息流要求，而关于后者的现有文献依赖于静态模型来生成和需求，这是限制性的。我们提出了一种新颖的控制方案，旨在通过在控制策略中利用发电量测量来克服这些问题。特别是，我们的控制器依赖于实际测量，并允许为广泛的线性发电动态范围推导出分布式稳定性和最优性保证，这可能是更高阶的。我们展示了如何通过求解适当的线性矩阵不等式 (LMI) 以计算有效的方式选择控制器参数。此外，我们通过使用真实的数值数据展示了所提出的分析如何应用于涡轮调速器动力学的各种示例。东北电力协调委员会 (NPCC) 140 总线系统的数值模拟证明了我们分析的实用性，该系统验证了我们提出的控制器与标称频率的收敛、经济上的最佳功率分配以及与使用的现有方案相比改进的性能在文献中。