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直流接地极地表电位的切比雪夫多项式求解法
Solving Surface Potential of DC Grounding Electrode by Chebyshev Polynomial
运行经验表明，直流接地极造成电网大范围直流偏磁危害其根源在不均匀地表电位分布。针对广域深度分层的复杂大地模型关于地表电位分布求解方面的难题，利用切比雪夫多项式拟合地表电位的汉克尔变换核函数。通过切比雪夫多项式的移位运算、系数展开和截断误差判定，得到了核函数的切比雪夫多项式自适应阶数拟合方法，从而大幅降低了直流接地极造成广大区域地表电位分布的计算难度。与标准接地计算软件CDEGS的水平8层结构大地算例对比表明，直流接地极入地电流5000A的情况下，方法在1km~100km地表范围内的地表电位偏差小于1V。进一步分析了切比雪夫多项式阶数对结果的影响，证实了20阶切比雪夫多项式的精度就可以满足一般的直流偏磁风险评估的应用需求。基于移位切比雪夫多项式的地表电位快速评估方法为直流偏磁风险评估提供了一种基础的技术手段，有助于降低电网直流偏磁风险评估的难度。
The operation experience shows that the root cause of the harm of large-scale DC magnetic bias caused by DC grounding electrode lies in the uneven surface potential distribution. The Chebyshev polynomial is used to fit the Hankel transform kernel function of surface potential in order to solve the problem of solving the surface potential distribution in the complex earth model of wide area depth stratification. Through the shift operation, coefficient expansion and truncation error determination of Chebyshev polynomial, the adaptive order fitting method of Chebyshev polynomial for kernel function is obtained, which greatly reduces the calculation difficulty of surface potential distribution in a large area caused by DC grounding electrode. Compared with the standard grounding calculation software CDEGS, the earth surface potential deviation is less than 1 V in the range of 1 km ~ 100 km when the DC grounding current is 5 000 A. The influence of the Chebyshev polynomial series on the results is further analyzed, and it is confirmed that the accuracy of the 20-order Chebyshev polynomial can meet the application requirements of the general DC bias risk assessment. The surface potential rapid assessment method based on the shifted Chebyshev polynomial provides a basic technical means for the risk assessment of DC bias, which is helpful to reduce the difficulty of risk assessment of DC bias in power grid.
直流接地极；地表电位；切比雪夫多项式；汉克尔积分；直流偏磁
DC grounding electrode; surface potential; Chebyshev polynomial; Hankel integral; DC bias
齐桓若
Qi Huanruo
国网河南省电力公司经济技术研究院
Economic and Technological Research Institute of State Grid Henan Electric Power Company
njqxxyxb/article/abstract/20211215002