随着我国电网规模的扩大和电压等级的升高，地磁暴产生的地磁感应电流(Geomagnetically Induced Current，GIC)对我国电网安全的威胁日益增大。现有研究在计算GIC时，存在大地电导率测量数据少，未测量区域多等问题，因此常假设电网所在区域的大地电导率为一恒定值，而这与实际情况不符，得到的GIC值也与实际值存在偏差。此外，地电场和电网参数等不确定性输入参数的变化也会对GIC产生影响，因此有必要以不确定性分析的角度来对GIC进行计算分析，可当不确定性输入参数维数较多时，现有不确定性分析方法又存在计算效率低下的问题。针对上述情况，本文对大地电导率模型和不确定性分析模型进行了改进并采用了高效方法对GIC进行了不确定性分析。本文的主要工作和研究结果如下所示：

首先，本文分析了四种大地电导率模型对地电场的影响，计算发现不同大地电导率模型会使地电场出现差异，进而影响到GIC的计算结果，因此有必要构建出更能反映真实大地电导率情况的模型。针对大地电导率模型构建过程中出现的测量数据少，且测量点之间存在大片未知区域的问题，本文给出了基于Kriging插值的大地电导率模型构建方法，并以华北地区的大地电导率测量数据进行了方法验证，验证结果表明，Kriging方法能够很好的对未知区域进行预测，弥补数据不足的同时能构建更符合实际情况的大地电导率模型，为下一步进行GIC不确定性分析奠定了基础。

其次，结合现有的GIC计算方法，本文给出了基于多项式混沌展开的地磁感应电流不确定性分析构建方法，并以1000 kV特高压输电网络为例，针对2004年11月17日到18日的地磁暴数据进行了GIC不确定性分析计算。计算结果表明：全阶展开法和回归法对多项式的基底和系数的计算优于张量积法和投影法；与蒙特卡洛方法相比，构建得到的多项式混沌展开模型在满足精度的前提下，能够极大的提高计算效率，并利用上述方法得到了GIC最大值的置信区间、均值和标准差等统计数据。分析数据后发现，华北1000 kV特高压电网的GIC分布不均，受地域特征影响明显，且随不确定性输入参数变化，各变电站GIC具有较大的变化范围。

最后，针对多维输入变量情况下，多项式混沌展开存在的项数过多，计算效率低下的问题，本文提出了基于压缩传感技术和高维模型表达的稀疏多项式混沌展开的构建方法。经计算验证，压缩传感技术能够很好的对多项式系数进行压缩处理，高维模型表达可以对多项式基底进行稀疏处理，综合上述两种方法能够提高计算效率，可以解决输入参数维数增加带来的维数灾难问题，并得到了多维不确定性输入参数下的GIC统计信息以及各变电站发生变压器局部过热的概率。基于方差分解法，本文还计算了各输入参数的灵敏度指标，将各不确定性输入参数对GIC变化的贡献程度进行了量化分析，灵敏度计算结果表明，地电场参数对GIC变化起主要作用，电网参数对GIC变化起次要作用。

本文的研究结果将为大地电导率建模和评估电网磁暴灾害风险提供参考，对制定合理的磁暴灾害防御策略具有重要意义。

With the expansion of the scale of Chinese power grid and the rise of voltage levels, the threat of geomagnetic induced current (GIC) generated by geomagnetic storms to the safety of my country's power grid is also increasing. When calculating GIC in existing studies, there are problems such as few data of ground conductivity measurement and many unmeasured areas. Therefore, it is often assumed that the ground conductivity of the area where the power grid is located is a constant value, which is contradictory to the actual situation. The obtained GIC The value must also deviate from the actual value. In addition, changes in uncertain input parameters such as geoelectric field and power grid parameters will also affect GIC, so it is necessary to calculate and analyze GIC from the perspective of uncertainty analysis, but the existing research on GIC uncertainty analysis is simple, and there is a problem of low computational efficiency for multi-dimensional input parameters. In view of the above situation, this paper improves the ground conductivity model and uncertainty analysis model, and conducts multidimensional uncertainty analysis on GIC. The main work and research results of this paper are as follows:

Firstly, this paper analyzes the influence of four earth conductivity models on the geoelectric field. It is found that different earth conductivity models will cause differences in the geoelectric field, which will affect the calculation results of GIC. Therefore, it is necessary to construct a model that can better reflect the real earth conductivity. Aiming at the problem that there is few measurement data in the process of building the ground conductivity model, this paper presents a ground conductivity model building method based on the Kriging method. And the method was validated with the earth conductivity measurement data in Northern China. The verification results show that the Kriging method can predict the unknown area very well, make up for the lack of data, and lay a foundation for the next step of GIC uncertainty analysis.

Secondly, combined with the existing GIC calculation method, this paper presents a construction method for the uncertainty analysis of GIC based on polynomial chaotic expansion. The calculation results show that: the full-order expansion method and the regression method are better than the tensor product method and the projection method in calculating the basis and coefficient of the polynomial; compared with the Monte Carlo method, the polynomial chaotic expansion model constructed can meet the accuracy requirements, can greatly improve the calculation efficiency, and use the above method to obtain the confidence interval, mean and standard deviation of the maximum value of GIC and other statistical data. After analyzing the data, it is found that the GIC distribution of the 1000 kV UHV grid in Northern China is uneven, which is obviously affected by regional characteristics, and varies with the uncertainty input parameters, and each substation has a large range of variation.

Finally, in the case of multi-dimensional input variables, polynomial chaos expansion has too many items and low calculation efficiency. This paper proposes a construction method of sparse polynomial chaos expansion based on compressed sensing technology and high-dimensional model representations. It is verified by calculation that compressive sensing technology can perform compression processing with polynomial coefficients very well， 安and high-dimensional model representations can be sparse on polynomial basis. Therefore, this article obtain the GIC statistical information and the probability of grid damage in each substation under the multi-dimensional uncertain input parameters. Based on the variance decomposition method, this paper also calculates the sensitivity index of each input parameter, and quantitatively analyzes the contribution of each uncertain input parameter to the change of GIC.

The research results of this paper will provide a reference for ground conductivity modeling and assessment of the risk of magnetic storm disasters in power grids, and are of great significance for formulating reasonable protection strategies for magnetic storm disasters.