延安地区雷电流幅值累积概率分布特征及计算公式

Distribution characteristics and calculation formula for cumulative probability of lightning current amplitude in Yan’an area

利用陕西省雷电定位系统资料分析了延安地区2009-2012年的雷电流数据,并对多种雷电流幅值累积概率公式进行了比较分析,同时引入雷电流概率密度公式,列举实例,分析了各累积概率公式所拟合的曲线与实测值所绘制曲线的误差,并根据分析结果给出了该地区带有未知系数α、β的雷电流幅值累积概率计算公式,利用Matlab的Cftool工具中的最小二乘曲线拟合方法对地闪进行拟合,求出拟合误差最小和拟合效果最好时的α、β值,得出了该地区更为精确的雷电流幅值累积概率计算公式,并利用该地区2013年的雷电流数据对推导出的公式进行了准确性验证.结果表明:正闪的平均雷电流幅值明显大于负闪,而负闪的雷电流幅值分布比正闪的分布相对更集中;正闪的雷电流幅值累积概率的分布曲线比较平缓,而负闪的相对比较陡峭;利用规程公式拟合的曲线与实测值对应的曲线差异较大,而利用IEEE Std和CIGRE推荐公式分别拟合的曲线与实测值对应曲线的变化趋势一致,相比规程公式IEEE Std的误差明显减小;当α=36.04,β=4.349时,拟合误差最小,拟合效果最好,并且发现雷电流I_c在0~150 kA时,拟合误差在-0.025~0.018,当Ic=35 kA时,拟合误差最大,为0.025,当Ic大于150 kA时,拟合误差趋于0.

Lightning current amplitude cumulative probability is a necessary parameter to characterize the frequency of thunder activity as well as calculate the lightning strike flashover.Using data from lightning location monitoring system in Shaanxi province,this paper analyses the lightning current data during 2009-2012 in Yan’an area,and compares various calculation formulas of cumulative probability for lightning current amplitude.Then the density formula is introduced,and an example is given to show the difference between the calculated and measured cumulative probability of lightning current amplitude.The least square curve fitting method of CFTOOL in MATLAB is employed to find the best fitting parameters,therefore a more precise calculation formula for lightning current amplitude cumulative probability is established.The lightning current data in 2013 is used to verify the proposed formula.Results show that the average current amplitude of positive lightnings is higher in value and less concentrated in distribution than that of negative lightnings.The distribution curve of lightning current amplitude cumulative probability is relatively flat for positive lightnings and steep for negative ones.As for the simulation results by various calculation formulas,the regular formula has the biggest error,while the formulas recommended by IEEE Std and CIGRE have similar variation trends and shapes compared with measured curves.The fitting is best with parameter α being 36.04 and β being 4.349;the fitting error is ranged in-0.025 to 0.018 when the lightning current(Ic) is from 0 to 150 kA,and decreased to close to 0 when Ic is more than 150 kA.Thus a more precise formula is established to calculate the cumulative probability of lightning current in Yan’an area,which is then verified through test.