不同地表情况下Cooray-Rubinstein算法的应用及其精度检验

Application and accuracy validation of the Cooray-Rubinstein formula for different soil conductivity

将雷电水平电场Cooray-Rubinstein(C-R)算法推广应用于地表电导率垂直分层的情况,并利用时域有限差分(FDTD)方法对不同地表情况下C-R算法的精度进行检验。结果表明,C-R算法的适用条件为:距离回击通道为100~1 000 m、地表电导率介于0.001~0.01 S/m,最大误差小于10%。当土壤电导率均匀分布时,C-R算法的精度最好;对电导率水平分层的情况,当上层电导率小于下层电导率时,C-R算法的精度较优;当电导率垂直分层时,若观测点处的土壤电导率小于闪击点处的电导率时,C-R算法的计算精度较高,反之,精度较低;对任何光滑有耗地表而言,利用C-R算法计算的首次回击水平电场的精度优于继后回击。

Lightning is a type of strong discharge phenomenon in nature which can radiate intensive electro magnetism pulses.The electro magnetism fields may couple into the overhead transmission lines or power installations lying underground and cause significant damage to power systems,so it is important to research the overvoltage caused by lightning.It is well known that there are three different yet equivalent field-to-transmission line coupling models,namely the model of Taylor,the model of Agrawal,and the model of Rachidi.Based on these models,the determination of induced currents and voltages requires the evaluation of specific field components depending on the employed coupling model.Among them,the accuracy of Agrawal coupling model has been proven by artificial triggering lightning experiments.In the model of Agrawal,the horizontal electric field component along the line is required.Considering the inherent difficulty in measuring lightning horizontal electric fields,namely for the observation points to be located on the ground or a few meters above the ground,the vertical electric field magnitude is much larger than that of the horizontal component（typically two orders of magnitude）,thus even a small tilt in the measurement sensor could render the measured horizontal field useless,and therefore it is necessary to create an accurate and efficient algorithm to obtain the results.The exact solution of the lightning horizontal field requires calculation of the Sommerfeld integrals for several elementary dipoles at many frequencies,which is very time consuming.The finite different time domain（FDTD） method is a numerical computation method which can be used to calculate the lightning-radiated horizontally electric field over different types of ground;however,the use of numerical calculations in this method will affect thememory,as well as time consumption.Therefore,it is necessary to develop a method to calculate the lightning-radiated horizontal electric field with high accuracy and rapid computation.The C-R formula is one approximation method by which to calculate the lightning-radiated horizontal electric field over homogeneous conductivity soil and horizontally stratified ground.In this paper we have extended the C-R formula to calculate the lightning-radiated horizontally electric field over vertically stratified soil conductivity based on the MTLL return stroke model and double-Herdler function base current,and have examined its accuracy over different types of ground by using the FDTD method.The results show that,when the distance between the lighting stroke point and observation point ranges from 100 m to 1 000 m,and the soil conductivity ranges from 0.001 S/m to 0.01 S/m,the error of the C-R formula is less than about 10%.For the homogeneous conductivity soil,the C-R formula achieves a more accurate prediction result than that for other soil conductivity cases;for the horizontally stratified soil,the accuracy of the C-R formula is better for the upper layer with less conductivity than that for the lower ground with higher conductivity;and for the vertically stratified ground,the accuracy of the C-R formula is better when the soil conductivity near the observation point is less than that near the strike point.Finally it can be concluded that the C-R formula can achieve a more accurate prediction result for the first return strokes than that for the subsequent return strokes.