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,其根源在地表电位不均匀分布.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结果表明,直流接地极入地电流5 kA时,本方法在1~100 km地表范围内的地表电位偏差小于1 V.进一步分析了切比雪夫多项式阶数对地表电位的计算结果的影响,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 experiences have shown that the large-scale DC magnetic bias caused by DC grounding electrode can be attributed to the uneven surface potential distribution.Here, the Chebyshev polynomial is used to fit the Hankel transform kernel function in order to solve the surface potential distribution for the complex earth model of wide area depth stratification.The adaptive order fitting method of Chebyshev polynomial for kernel function is obtained via shift operation, coefficient expansion and truncation error determination, 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 proposed Chebyshev polynomial approach achieves less than 1 V of earth surface potential deviation in range of 1-100 km when the DC grounding current is 5 000 A.Moreover, the order of the Chebyshev polynomial has influence on the solution results, and it is confirmed that the 20th-order Chebyshev polynomial can meet the accuracy requirements for general DC bias risk assessment.The proposed surface potential assessment method based on shifted Chebyshev polynomial provides a basic technical means for the risk assessment of DC bias, which is helpful to reduce the difficulty of DC bias risk assessment for power grid.