太阳活动会引发地球磁场强度和方向发生急剧且不规则的变化，称为地磁暴。地磁暴作用于电网会产生地磁感应电流(Geomagnetically Induced Current, GIC)，GIC流过变压器中性点，会引起变压器无功损耗增加，导致某些元件退出运行，系统潮流重新分配，进而引发连锁故障。随着电网规模的不断扩大，电网一旦发生连锁故障将会导致大停电事故。母线跳闸和线路开断是引发连锁故障的重要源发性故障，因此，如何准确识别地磁暴作用下电网关键节点及预测连锁故障对电网的安全稳定运行与地磁暴灾害防治具有重要意义。本文针对以上问题进行了研究，主要工作及成果如下：

首先，建立了GIC及变压器无功损耗计算模型，分析了计算过程中的不确定输入参数并确定了各参数的变化范围。基于多项式混沌展开方法对GIC及变压器无功损耗进行不确定性分析，基于方差分析的全局敏感性方法对不确定参数作用下的敏感性进行量化。以IEEE RTS79系统为例，验证了所提方法的有效性和高效性的同时得到了均值、95%置信区间等统计信息，为下文关键节点识别及连锁故障预测提供了数据支持。

其次，提出了两种考虑地磁暴影响的关键节点识别方法。在传统LeaderRank算法的基础上，考虑节点度数、线路潮流等因素量化节点间相互关系，并将地磁暴引入背景节点与算法有机结合，提出了改进的LeaderRank算法；在节点中心性的基础上，结合电网拓扑结构及系统潮流，引入地磁暴参数，提出了考虑地磁暴影响的改进节点电气中心性算法。以IEEE RTS79系统为例，对不同地电场作用下的关键节点进行识别，两种方法相互印证，验证了所提关键节点识别方法的有效性，为下文连锁故障预测奠定了基础。

最后，基于复杂系统脆性理论对电网进行脆性分析，建立了地磁暴作用下电网连锁故障预测模型，提出了通过关键节点确定故障链初始故障，通过脆性关联度及过载系数确定故障链中间环节的方法。采用模糊综合评估方法从发生概率和后果严重度两个方面对故障链风险等级进行划分。所得结果可用于量化评估地磁暴灾害风险，为后续地磁暴的预防与治理提供参考。

Solar activity triggers sharp and irregular changes in the strength and direction of the Earth's magnetic field, known as geomagnetic storms. The geomagnetic storm acts on the power grid to generate geomagnetically induced current (Geomagnetically Induced Current, GIC). GIC flows through the neutral point of the transformer, which will cause the reactive power loss of the transformer to increase, cause some components to stop running, redistribute the system power flow, and cause cascading failures. As the scale of the power grid continues to expand, once a cascading failure occurs in the power grid, it will lead to a major blackout. Bus tripping and line disconnection are important source faults that cause cascading faults. Therefore, how to accurately identify the critical nodes of the power grid under the action of geomagnetic storms and predict cascading faults has important significance for the safe and stable operation of the power grid and the prevention and control of geomagnetic storm disasters. This paper conducts research on the above issues, and the main work and achievements are as follows.

Firstly, the calculation model of GIC and transformer reactive power loss is established, the uncertain input parameters in the calculation process are analyzed and the variation range of each parameter is determined. Based on the polynomial chaos expansion method, the uncertainty analysis of GIC and transformer reactive power loss is carried out, and the global sensitivity method based on variance analysis is used to quantify the sensitivity under the action of uncertain parameters. Taking the IEEE RTS79 system as an example, the effectiveness and efficiency of the proposed method are verified, and statistical information such as the mean value and 95% confidence interval are obtained, which provides data support for the identification of critical nodes and the prediction of cascading failures below.

Secondly, two critical node identification methods considering the influence of geomagnetic storm are proposed. On the basis of the traditional LeaderRank algorithm, considering factors such as node degree and line flow to quantify the relationship between nodes, and introducing geomagnetic storms into background nodes and organically combining the algorithm, an improved LeaderRank algorithm is proposed; on the basis of node centrality, combined with power grid topology and system power flow, introducing geomagnetic storm parameters, proposed an improved node electrical centrality algorithm considering the impact of geomagnetic storms. Taking the IEEE RTS79 system as an example, the critical nodes under different geoelectric fields are identified. The two methods are mutually verified, which verifies the effectiveness of the proposed critical node identification methods and lays the foundation for the following cascading fault prediction.

Finally, based on the brittleness analysis of the power grid based on the brittleness theory of complex systems, a prediction model of cascading faults in the power grid under the action of geomagnetic storms is established, and a method of determining the initial fault of the fault chain through critical nodes and determining the intermediate link of the fault chain through the brittle correlation degree and overload coefficient is proposed. The fuzzy comprehensive evaluation method is used to divide the risk level of the fault chain from two aspects of occurrence probability and consequence severity. The obtained results can be used to quantitatively assess the risk of geomagnetic storm disasters, and provide reference for the prevention and control of subsequent geomagnetic storms.

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