One of the priority tasks in studying power grids is to find the conditions of their stable operation. The fundamental requirement is synchronizing all the elements (generators and consumers) of a power grid. However, various disturbances can destroy the synchronization. Moreover, desynchronization occurring in a small part of the grid can lead to severe large-scale power outages (or blackouts) due to numerous cascading failures. Here we consider the model of a heterogeneous power grid with hub structures (subgrids), taking into account arbitrary lengths and impedances of grid’s transmission lines and also their arbitrary amount. Using the auxiliary comparison systems approach, we analyze the dynamics of a hub subgrid. Based on the findings, we develop a novel criterion of partial stability of power grids featuring hub structures. The criterion makes it possible to identify the regions of safe operation of individual hub subgrid elements. First, the criterion allows obtaining parameters’ values that guarantee existence and local stability of either synchronous or quasi-synchronous modes in individual hub subgrid elements, i.e. steady-state stability. Second, the criterion allows obtaining the safe values of abrupt frequency and phase disturbances that eventually vanish, i.e. imply transient stability with respect to state disturbance. Third, the criterion permits determining the safe ranges of parameters’ disturbances that do not lead to catastrophic desynchronizing effects, i.e. imply transient stability with respect to parameters’ disturbance. Also, we discover typical dependences of the safe regions on the parameters of transmission lines. We demonstrate the applicability of the criterion on two test power grids with arbitrary distributions of powers as well as effective lengths and impedances of transmission lines. The results may help optimize stability and contribute to developing new real-time control schemes for smart grids that can automatically recover from failures.

研究电网的首要任务之一是寻找其稳定运行的条件。基本要求是同步电网的所有元素（发电机和消费者）。然而，各种干扰都会破坏同步。此外，由于大量的级联故障，电网的一小部分发生不同步会导致严重的大规模停电（或停电）。在这里，我们考虑具有枢纽结构（子电网）的异构电网模型，考虑到电网传输线的任意长度和阻抗以及它们的任意数量。使用辅助比较系统方法，我们分析了枢纽子网格的动态。基于这些发现，我们开发了具有枢纽结构的电网局部稳定性的新标准。该标准可以识别单个枢纽子电网元素的安全运行区域。首先，该准则允许获得参数值，以保证单个枢纽子网格元件中同步或准同步模式的存在和局部稳定性，即稳态稳定性。其次，该标准允许获得最终消失的突然频率和相位扰动的安全值，即暗示相对于状态扰动的瞬态稳定性。第三，该准则允许确定不会导致灾难性去同步效应的参数扰动的安全范围，即暗示关于参数扰动的暂态稳定性。此外，我们发现安全区域对传输线参数的典型依赖性。我们证明了该准则在具有任意功率分布以及传输线的有效长度和阻抗的两个测试电网上的适用性。结果可能有助于优化稳定性，并有助于为智能电网开发可自动从故障中恢复的新实时控制方案。