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The impulse voltage wave invading a transformer is not the double exponential impulse wave (DEIW) specified by the IEC but a non‐standard waveform with oscillation attenuation characteristics, and this fact leads to doubts about the scientificity and optimality of insulation coordination. A key solution for this issue is the establishment of an equivalent relationship between the measured non‐standard impulse voltage wave and the DEIW. In this study, a test platform of multiparameter impulse voltage was set up. Then, the authors obtained the 50% breakdown voltage (U50%) of the oil‐impregnated paper (OIP) for transformer under the bipolar oscillatory attenuated impulse wave (BOAIW) and the DEIW with different waveform parameters. The effects of waveform parameters on the breakdown characteristics of the OIP were finally revealed. On the basis of experimental data and several mathematical methods, the authors established the U50% prediction mathematical models for the OIP under the BOAIW and DEIW. Based on the prediction models and the microfluctuation characteristics of measured overvoltage's waveform parameters, the authors proposed a method for evaluating the waveform equivalence. The characteristics of voltage amplitude and change rate were regarded as the two key factors for the waveform equivalence of this method. [ABSTRACT FROM AUTHOR]