变电站内水平多层土壤参数反演

Parameter Estimation of Horizontal Multi-layer Earth in Substation

接地网是变电站的重要组成,起到保障变电站设备安全运行和工作人员安全的作用。IEEE Std80-2000指出,变电站内水平多层土壤的参数分布特性对接地网的接地性能有很大影响。视在电阻率是直接反映水平多层土壤参数的电学指标,因此基于Wenner法建立水平多层土壤的视在电阻率模型是研究其参数特性的重要手段。基于点电流源在水平多层土壤中满足的泊松方程和边界条件,建立了广义积分形式的视在电阻率计算公式;结合Prony展开式和Lipschitz积分得出了有限项求和形式的视在电阻率复镜像表达式。利用视在电阻率测量值和计算值间的均方根误差函数建立了水平多层土壤参数反演模型。采用改进粒子群算法(improved particle swarm optimization,IPSO)拟合不同电极间距离d情况下视在电阻率;优化过程结束后,最小适应度函数对应的粒子被作为最优土壤参数输出。通过与已发表论文中水平两层和三层土壤参数模型对比,验证了所提算法在反演水平多层土壤参数时是有效、可行的。此外,由于测量的视在电阻率是在d>10t(d为电极间距,t为电极入地深度)假设下进行简化得出的,所以提出剔除d<1 m时无效的视在电阻率测量值的方法来提高水平多层土壤参数估计的精度,该方法也能够对采用Wenner法的视在电阻率现场测量提出指导意见。

Ground grid has great significance for substations. IEEE Std80-2000 points out that the characteristics of horizontal multilayered earth parameters have a great influence on the grounding performance of ground grids. Apparent resistivity is the direct electrical index, and its mathematical model based on Wenner method is an important means to study earth parameters, the corresponding formula in a generalized integral form can be established utilizing Poisson＇s equation and the boundary conditions of point current source in multi-layered soil. With the combination of Prony expansion and Lipschitz integration, the equation for fast computation of apparent resistivity is deduced with the summation of limited polynomial terms. Afterwards, improved particle swarm optimization（IPSO） was adopted to solve the horizontal multi-layered earth model using the measured apparent resistivity while the fitness function is chosen as the RMSE between the measured and computed apparent resistivity. In the end of optimization, the particles corresponding to the minimized fitness function were output as the optimal earth parameters. Compared with those published algorithms, IPSO was verified by two-and three-layered earth model, which demonstrate that it is more effective and feasible to obtain horizontal multi-layered earth parameters. The equation of measured apparent resistivity is simplified under the assumption of d10t（d is electrode spacing and t is electrode buried depth）, therefore, the measured apparent resistivity with respect to d1 m is invalid and can be removed, which can promote the precision of estimated earthparameters and provide the guidance for measuring apparent resistivity.