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An effective means of rationalization of insulation design for gas insulated switchgear (GIS) is the evaluation of insulation characteristics under actual surge waveforms in the field called non-standard lightning impulse waveforms (non-standard-LIWs). The preceding researches examined quasi-uniform electric field SF6 gas gaps and partly the cone-shaped insulating spacers that represent an insulation element of GIS in order to obtain the insulation characteristics under various non-standard-LIWs. As a result, the breakdown voltages under non-standard-LIWs are higher than those under standard-LIWs, allowing the authors to identify a road map for rationalizing GIS insulation designs. In applying this rationalization technique, experimental study was conducted on single-frequency oscillations to identify the influence of the non-uniform electric field. As a result, the breakdown characteristics were found to be different from those in a quasi-uniform electric field. This paper describes the insulation characteristics under double-frequency oscillations as typical examples of nonstandard-LIWs while varying the applied voltage polarities, frequencies, and damping factors in order to study the influences of non-uniform electric field in further detail. The experimental results show that positive-polarity waveforms pose more demanding insulation requirements and that it is appropriate to conduct experiments using positive-polarity in order to consider dielectric strengths. Moreover, it was confirmed that changing the waveform parameters under positive-polarity did not cause major changes in the breakdown voltages, which remained constantly higher than those under standard-LIWs, and gave little influence to the application of the rationalization techniques.