During its operation, electrical equipment is constantly exposed to overvoltages of various waveforms, such as lightning discharges, switching operations, faults, etc. Therefore, adequate selection of overvoltage protection and equipment insulation withstand voltages are key factors in increasing system reliability. In general, insulation coordination is carried out by analyzing the insulation behavior for standard impulse and switching overvoltage waveforms. However, overvoltages that occur in operating conditions can significantly deviate from the standard waveforms of insulation withstand voltages, in terms of the front time, the duration of the wave, the existence of highfrequency components as result of reflections in the facility and other factors. This paper presents possible methods of assessing the behavior of equipment insulation for real voltage waves to which the insulation is exposed during exploitation and which deviate from standard waveforms, by analysis in the frequency domain. As there are different components in the overvoltage signal at different frequencies, which a different energy, the main goal of this paper is to analyze the insulation characteristics of a specific transformer from the point of view of the energy spectral density of the voltage wave that occurs at its terminals when an atmospheric discharge occurs. The analysis is based on the determination of the safety margin on the entire frequency spectrum of the overvoltage wave, that is, on the calculation of the so-called FDSF (Frequency Domain Severity Factor). The calculation results show that although the overvoltage amplitude is lower than the withstand voltage of the transformer insulation with an appropriate safety margin (the condition of the classic approach to insulation coordination is satisfied), the spectrum analysis of the voltage wave in the frequency domain shows that the insulation may still be compromised.