## 2 Overview of the Frequency Dielectric Spectroscopy Measurement and Domain Method  
Due to the limitations associated with DC insulation testing methods used for high-voltage transformers, research since the year 2000 has increasingly focused on analyzing the polarization responses of dielectric materials within power equipment under varying AC voltage signals. The fundamental principle behind frequency dielectric spectroscopy (FDS) is based on observing the physical responses of dielectric particles to input signals within a specific frequency range from very low to moderate frequencies (1 mHz to 10 kHz). Compared to other diagnostic methods, a significant advantage of FDS is its ability to individually analyze the insulation conditions of electrical equipment containing oil-paper insulation, specifically evaluating the solid insulation separately from the transformer oil [12,13]. Nevertheless, the FDS method itself has notable drawbacks. It exhibits high sensitivity to internal temperature variations within the transformer and to geometric configurations. Additionally, another significant limitation is the considerable duration required for comprehensive measurements, which can exceed three hours at extremely low frequencies (from 0.1 mHz). Driven by multiple experimental studies, one of the primary objectives of our research on FDS is to mitigate the impact of temperature sensitivity within this diagnostic technique. The FDS method is a critical diagnostic tool for assessing the insulation conditions of high-voltage equipment utilizing oil-paper insulation. This method evaluates the insulation system's response, expressed through parameters like loss factor or capacitance, across a theoretical frequency range from 0.0001 Hz up to 10 kHz. Initially developed in the late 1990s, FDS was applied primarily to measure oil conductivity and the moisture content within solid insulation materials in high-voltage transformers and cables [14,15]. Previous research focused on electrical insulation condition monitoring has identified frequency domain spectroscopy as the most widely used technique for evaluating the deterioration of oil-paper insulation in power transformers. The inclusion of very low-frequency measurements (down to approximately 0.1 Hz) is essential for accurately detecting moisture levels, as these frequencies strongly correlate with moisture content. Alongside frequency sweep assessments, experimental analyses involving dielectric responses to varying voltage levels have also been performed and discussed extensively [14]. The focus lies in evaluating and comparing modern dielectric spectroscopy methods with traditional measurement techniques, such as dielectric absorption ratio, polarization index, and dielectric dissipation factor assessments conducted at power frequency and at 0.1 Hz. Conventional methods often exhibit limitations due to restricted time and frequency ranges, complicating the distinction among various dielectric properties [16; 17]. When sinusoidal voltage is applied to insulation comprising both resistive and capacitive components, the resulting current passing through the insulation will also consist of resistive and capacitive components shifted by a particular phase angle \(\varphi\). The dissipation angle \(\delta\) represents the angular difference between this resultant current and the imaginary axis. It quantifies how much the insulation deviates from ideal capacitive behavior, where the current would be purely capacitive. Insulation without losses occurs when the phase angle \(\varphi\) equals 90\({}^{\circ}\), corresponding to a dissipation angle \(\delta\) of 0\({}^{\circ}\)[18].