Aiming at the uneven voltage distribution of the top-wires insulator string on a very low frequency transmitting antenna under high voltage

which can easily produce corona

the voltage distribution of the porcelain insulator string is calculated by the method of moments（MOM） for different tube diameters

radiuses

and elevation distances of the grading ring and configuration positions of the insulator string.A novel method based on MOM and butterfly mating optimization（BMO） is proposed for optimizing the grading ring of the top-wires insulator string.First

an MOMbased antenna optimization model for the top-wires insulator string is established.Then

the voltage distribution and antenna efficiency are obtained by simulation

and the fitness function is calculated.BMO is used to iteratively optimize the deploying location and the grading ring structure of the top-wires insulator.Simulation results show that the radius and elevation distance of the grading ring on high-voltage side have great influences on the voltage distribution of the insulators.The partial voltage on the end of the insulator string can be reduced by 44.5% if deploys a grading ring on the low-voltage side.Compared with the measured values before optimization

the mean square error of voltage distribution of the optimized insulator strings decreases by 2.17%

the maximum surface electric field of the grading ring is less than the electric field of corona inception

and the radiation efficiency of the antenna increases by 1.5%.