标题： 区域振荡的矩阵摄动理论 显示英文标题

标题： Matrix Perturbation Theory of Inter-Area Oscillations

摘要： 互联电力系统具有许多优势，例如更好的电能质量、供电的更高可靠性、通过生产和备用池实现的规模经济等。 同时，随着所谓的区域间振荡的出现，可能会危及整个系统的稳定性，这些振荡是涉及相隔数千公里的大范围旋转设备的相干振荡。 这些通常阻尼较弱的模式可能对电网运行产生有害后果，尽管经过数十年的研究，生成这些模式的机制仍然不甚清楚，现有的理论基于在实际电力网络中观察到这些模式时并不满足的假设。 在这里，我们构建了一个大型互联电力系统的矩阵扰动理论，以阐明区域间振荡的起源和出现条件。 我们表明，相干的区域间振荡源自多区域网络拉普拉斯矩阵的零模，即使在区域间联络线容量较大的情况下，这些零模与其他模式的混合也很弱，即当标准的区域划分假设不成立时也是如此。 该通用理论在一个两区域系统上进行了说明，并数值应用于欧洲同步电网的连接良好的PanTaGruEl模型。 显示英文摘要

摘要： Interconnecting power systems has a number of advantages such as better electric power quality, increased reliability of power supply, economies of scales through production and reserve pooling and so forth. Simultaneously, it may jeopardize the overall system stability with the emergence of so-called inter-area oscillations, which are coherent oscillations involving groups of rotating machines separated by large distances up to thousands of kilometers. These often weakly damped modes may have harmful consequences for grid operation, yet despite decades of investigations, the mechanisms that generate them are still poorly understood, and the existing theories are based on assumptions that are not satisfied in real power grids where such modes are observed. Here we construct a matrix perturbation theory of large interconnected power systems that clarifies the origin and the conditions for the emergence of inter-area oscillations. We show that coherent inter-area oscillations emerge from the zero-modes of a multi-area network Laplacian matrix, which hybridize only weakly with other modes, even under significant capacity of the inter-area tie-lines, i.e. even when the standard assumption of area partitioning is not satisfied. The general theory is illustrated on a two-area system, and numerically applied to the well-connected PanTaGruEl model of the synchronous grid of continental Europe.