Sensitivity analysis of geomagnetically induced current based on hyperbolic scheme for truncating polynomial chaos expansion
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摘要: 地磁感应电流(GIC) 可能会引起变压器直流偏磁从而威胁电力设备和电网的安全。鉴于GIC计算所需的很多输入参数是不确定变量, 全面评估电网GIC水平及对电网的威胁有必要研究GIC的不确定度及GIC对输入变量的敏感度。基于混沌多项式展开(PCE) 提出了一种GIC的不确定度量化方法, 利用双曲线截断技术进一步提高了计算效率, 计算了GIC对输入参数的敏感度指标。以新疆750kV规划电网为例, 利用提出的方法对GIC进行了不确定度量化, 得到了GIC的均值和标准差等统计量。根据混沌多项式系数计算了Sobol敏感度指标, 得到了GIC对电场幅值和电网直流电阻等输入参数的敏感度。与蒙特卡罗法(MC) 相比, 此方法在保证精度的前提下大大提高了计算效率。Abstract: Geomagnetically Induced Current (GIC) can cause DC bias of the transformer.The derivative effect of DC bias may threaten the safety of power equipment and power grid.In view of the fact that many input parameters are uncertain variables in GIC calculations, it is necessary to study the uncertainty of GIC and the sensitivity of GIC to input variables.In this paper, based on polynomial chaos expansion (PCE) and hyperbolic scheme for truncating the polynomial chaos expansion, a GIC uncertainty quantization method is proposed.Using the constructed polynomial chaos expansion, the sensitivity index of GIC to input parameters is derived.For the planned Xinjiang power grid, the proposed method is used to measure the uncertainty of GIC, and the statistics of mean and variance of GIC are obtained.The Sobol sensitivity index is calculated according to the chaotic polynomial coefficient, and the sensitivity of GIC to input parameters such as electric field amplitude and grid DC resistance is obtained.Compared with the Monte Carlo method (MC), this method is not only precise, but also greatly improves the computational efficiency.
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图 2 参数对I影响的PC与MC方法对比
Figure 2. Comparison of GIC in the substations by PC and MC method
图 3 双曲线截断的PCE与MC方法结果对比
Figure 3. Comparison of GICs in substations by hyperbolic scheme for truncating the PCE and MC methods
图 4 双曲线截断的PCE与MC方法结果对比
Figure 4. Comparison of GICs in substations by hyperbolic scheme for truncating the PCE and MC method
图 6 电网参数和电场敏感度分析结果
Figure 6. Results of sensitivity of grid parameters and electric field
表 1 PCE和MC方法的运行结果对比
Table 1. Operating result comparison of PCE and MC
substation mean current/A standard deviation time/s MC SRSM Galerkin MC SRSM Galerkin MC SRSM Galerkin Hetian 212.149 5 212.145 3 212.149 3 10.833 8 10.844 5 10.828 4 52.72 6.07 8.13 Kashi 175.208 7 175.195 6 175.197 7 10.900 1 10.913 7 10.899 2 Tulufan 104.987 8 104.999 7 105.001 3 4.635 6 4.629 8 4.629 3 Wubei 62.446 0 62.456 0 62.456 6 2.973 2 2.968 3 2.969 5 
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