Research On High Precision Fast BEM And Its Application In Insulator Electric Field Calculation

Along with the power system transmission voltage grade increasing the higher request to the safety of insulator is brought forward, therefore to study the distribution of the electric potential and electric field intensities of the insulator has the important actual meanings. Aimed at increasing the accuracy and speed of BEM, meanwhile decreasing taken up memory, this dissertation has studied singular integrals and nearly singular integrals of BEM, surface BEM character and multipole BEM delaminating and storing technology, and put forward high precision fast BEM. And appling this method the electric potential and electric field intensities distribution of the UHV insulators are calculated preliminarily. The main achievements are as follows:1. The equations of DBEM and IBEM have systematically been deduced which can apply in electrodes, multi-dielectrics and multi-floating-conductors. Especially in IBEM the floating-conductor is equivalent to dielectric with infinite permittivity. And don't need additional constraint equations.2. A set of analytical integral method of triangular element linear interpolation BEM has systematically been deduced and put forward. By this method the errors caused by nearly singular and singular integrals are eliminated. This method is particularly applicable to sheet metal and narrow seal which have prominent singularities.3. Aimed at spherical, cylindrical, conical and toroidal electrodes in electrical engineering, based on the corresponding coordinate transformation the randomly meshing surface BEM is put forward. In this method, the precision is improved from three aspects of unknown interpolation, integral region and normal directions. The calculating results show that compared with one-order and two-order BEM in rectangle system, on the condition of the same meshing nodes the precision of the surface BEM is obviously higher; and on the condition of the same precision the surface BEM requires less nodes, consequently required memory and calculated time can be decreased greatly.4. In the course of delamination of MLFMA BEM the saving memory technique and fast delaminating method are presented. In delaminating course three one-dimension arrays substitute for a four-dimension array, thus the memories are saved greatly. The total elements are assigned into boxes of a certain layer of some top's. In downward delaminating course because only elements in correlating box are judged the speed is fast. The calculating results show that in PC of 1G memory the unknowns can reach three millions by MLFMA BEM.5. Combined surface BEM with multipole technique, the surface multipole BEM is put forward. In calculating multipole coefficients the surface integrals on actual boundary are adopted. Hence the adventages of high precision surface BEM and fast multipole technique are fully utilized.6. Aimed at electrical field calculation the high precision fast BEM software package is developed elementarily. Making use of this software package the insulator string electric field distribution is calculated preliminarily.